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Strict practical stability of nonlinear impulsive systems by employing two Lyapunov-like functions. (English) Zbl 1156.34329

Summary: This paper develops the concepts of strict practical stability of ordinary differential equations to impulsive differential system. Strict practical stability, known as stability in tube-like domain, can be made to estimate upper bound and lower bound of the solutions of impulsive differential equations. This note provides several stability criteria for strict practical stability of nonlinear dynamical systems with impulse effects by employing two Lyapunov-like functions under general restrictions. It may provide a greater prospect to solve problems which exhibit impulsive effects.

MSC:

34D20 Stability of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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